Please answer the following questions
Heat Power is a utility company that would like to predict the monthly heating bill for a household in a particular region during the month of January. A random sample of 18 households in the region were selected and their January heating bill recorded. The data is shown in the table below along with the square footage of the house (SF), the age of the heating system in years (Age), and the type of heating system (Type: heat pump = 1 or natural gas = 0). Household Bill SF Age Type $255 2,070 7 Natural Gas AWN $286 1.909 17 Natural Gas $296 2.004 8 Natural Gas $300 2.307 22 Natural Gas $305 3.021 5 Natural Gas $317 2.683 14 Natural Gas $321 1,511 8 Natural Gas $321 2,836 Natural Gas 9 $339 2,553 20 Natural Gas 10 $349 2.497 11 Natural Gas 11 $369 2,103 12 Heat Pump 12 $374 2.486 18 Heat Pump 13 $381 2,279 19 Heat Pump 14 $413 2,477 17 Heat Pump 15 $419 3.218 11 Heat Pump 16 $441 3.080 8 Heat Pump 17 $522 2,507 20 Heat Pump 18 $560 3.517 18 Heat PumpSUMMARY OUTPUT Regression Statistics Multiple R 0.8655 R Square Adjusted R Square Standard Error 44.8082 Observations 18 ANOVA of MS F Significance F Regression 3 83,948.96 Residual 14 28,108.82 Total 17 112,057.78 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 144.7200 65.1807 2.2203 0.0434 4.921 284.519 SF 0.0583 0.0237 2.4648 0.0273 0.008 0.109 Age 2.4158 2.0074 Type 95.0806 24.7518 3.8414 0.0018 41.993 148.168 Question 44 (1 point) Which of the following statements about multiple regression model building is true? )Both stepwise and best subsets methods check assumptions and conditions. ()The best subsets method will involve trying fewer different regression models than stepwise regression. There is no simple definition of the "best" model in multiple regression analysis. Stepwise selection will always find the best regression model. There is only one criterion, the R" value, that leads to the best model.Question 45 (1 point) Which of the following statements does not describe a point with high leverage? O The leverage can be negative. O A point of high leverage may not influence the regression slope. O A point with zero leverage has no effect on the regression slope. O A point may exert high leverage because it has an unusual combination of predictor values. A point with high leverage is easy to see in a regression of a single predictor and response. Question 46 (1 point) In order to determine whether collinearity may be an issue in the regression model, we should use: O Leverage Index. Standardized Residuals. O Cook's Distances. O Coefficient of Determination. O Variance Inflation Factors.Question 47 (1 point) Based on the regression output above, which of the following regression equations would help predict the monthly heating bill for a household in the region during the month of January? Consider the following notation for the different predictor variables in the model: square footage of the house (X 1), the age of the heating system(X 2), and the type of heating system(X 3). O y=144.72+0.0583y1 +2.4158y2+95.0806y3 OV=144.72+0.0583X1+2.4158X2+95.0806X3 O y=0.0583X1+2.4158X2+95.0806X3 O y=144.72+0.0583X1+2.4158X2+95.0806X3 Question 48 (3 points) Which of the following interpretations is/are valid for the meaning of the regression coefficients for the heating bill model above? You can select one or more answers. On average, the monthly heating bill is $144.72 for the houses located in this region. Each additional year in the age of the heating system increases the monthly heating bill by an average of $2.4158, when the other variables remain the same. Each additional square foot of the house increases the monthly heating bill by an average of $0.0583, when all the other variables remain the same. Houses that have a heat pump have heating bills that average $95.806 more than houses with natural gas, when all the other predictors are held constant.Each additional year in the age of the heating system increases the monthly heating bill by an average of $2.4158, when the other variables remain the same. Each additional square foot of the house increases the monthly heating bill by an average of $0.0583, when all the other variables remain the same. )Houses that have a heat pump have heating bills that average $95.806 more than houses with natural gas, when all the other predictors are held constant. Question 49 (1 point) Based on the regression output above, the average monthly heating bill for a 2,600 sq. ft. house with a heat pump that is 9 years old is predicted to be: Round your answer to two decimal places. Question 50 (2 points) Which of the following is an approximate 95% confidence interval for the average monthly heating bill for a 2,600 sq. ft. house with a heat pump that is 9 years old? Assume that SE Fit is 20.8071 and interval half width for average predicted Y is 44.62688. O ($223.808, $313.061) O ($272.722, $463.608) O ($368.528, $457.781) O ($307.194,$519.114)Question 50 (2 points) Which of the following is an approximate 95% confidence interval for the average monthly heating bill for a 2,600 sq. ft. house with a heat pump that is 9 years old? Assume that SE Fit is 20.8071 and interval half width for average predicted Y is 44.62688. O ($223.808, $313.061) O ($272.722, $463.608) ($368.528, $457.781) O ($307.194,$519.114) Question 51 (2 points) Which of the following is a 95% prediction interval for the monthly heating bill for a specific house that has 2,600 square feet and a heat pump that is 9 years old? Assume that SE Fit is 20.8071 and interval half width for individual response Y is 105.9601. ($307.19, $519.11) )The regression equation is for the average monthly heating bill, thus the monthly heating bill for a specific house cannot be computed. O ($223.808,$313.061) ($368.528,$457.781)Question 52 (1 point) The percentage amount of the variation in a household's monthly heating bill is explained by the square footage of the house, the age of the heating system in years, and the type of heating system (heat pump or natural gas) is: Round your answer to two decimal places. Question 53 (1 point) Which of the following is the correct hypothesis for testing whether the regression model above is worthwhile? OHo = B1 = B2 = 0 H1 = at least Bi or B2 # 0 O Ho = B1 = 0 H1 = B1 # 0 O Ho = P1 = P2 = p3 = 0 Hi = at least two coefficient correlations pi # 0 OHo = B1 = B2 = B3 = 0 H1 = at least one Bi # 0
